In this section we present a convergence analysis for \(\phi \) -critical points of Tikhonov-type functionals \(\mathcal {T}_{\alpha , y^\delta }\)  extending the existing analysis for global minima [1]}.
At this point we want to emphasize again that the assumption of being able to obtain global minima of \(\mathcal {T}_{\alpha , y^\delta }\)  can be extremely restrictive when \(\mathcal {R}\)  is non-convex and the main goal of our analysis is to discard this assumption. Instead we focus only on \(\phi \) -critical points of \(\mathcal {T}_{\alpha , y^\delta }\)  which may include local minimizers, saddle points or even local maxima.
